Colóquio de Matemática – 10/mai/2024
Palestrante: Prof. Dr. Maicon Marques Alves (UFSC)
Data: 10 de maio de 2024
Horário: 14h
Local: Auditório Airton Silva
Título: A search-free O(1/k^{3/2}) homotopy inexact proximal-Newton extragradient algorithm for monotone variational inequalities
Resumo: We present and study the iteration-complexity of a relative-error inexact proximal-Newton extragradient algorithm for solving smooth monotone variational inequality problems in real Hilbert spaces. We removed a search procedure from Monteiro and Svaiter (2012) by introducing a novel approach based on homotopy, which requires the resolution (at each iteration) of a single strongly monotone linear variational inequality. For a given tolerance ρ > 0, our main algorithm exhibits pointwise O(1/ρ) and ergodic O(1/ρ^{2/3}) iteration-complexities.
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